Coordinating Swarms of Objects at Extreme Dimensions

We describe a variety of algorithmic challenges arising from coordination and reconfiguration of swarms of potentially many objects, ranging in size from minuscule particles all the way to far-away satellite swarms. Particular results include methods for coordinating the motion of vehicles in traffic in order to avoid inefficient stop-and-go congestions; using uniform global forces for controlling particle swarms; online triangulation and structured exploration; cohesive control for swarms of robots with only local communication; coordinated motion planning for efficiently reconfiguring an arrangement of robots; and constructing and reconfiguring large-scale structures by finite automata. All presented work is based on collaborations with a variety of authors, who are named in the respective sections of this overview.